W. Feller. Proceedings of the conference on differential equations
(dedicated to A. Weinstein), стр. 251--270. University of Maryland Book Store, College Park, Md., (1956)
W. Feller. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, стр. 227--246. Berkeley and Los Angeles, University of California Press, (1951)
D. Kendall. Biometrika, (1948)The author discusses a ``birth-and-death process'' for which the Kolmogorov differential equations assume the form $$ P_n'(t)=-n(a+b)+cP_n(t)+(n-1)a+cP_n-1(t)\\ +(n+1)bP_n+1(t), $$ where $P_n(t)$ is the probability of a population size $n$. The case $c0$ corresponds to mortality and fertility proportional to the actual population size. The $c$-term accounts for an increase by immigration. The generating function of $P_n(t)$ is obtained and it is shown that for small $c$ one obtains approximations to R. A. Fisher's ``logarithmic series distribution'' which has found several applications in biology..
A. Kolmogorov. Izv. Akad. Nauk SSSR, Ser. Math, (1937)Computes density of fairly general Johnson-Mehl crystals and the probability that a point is not in a crystal yet..
J. Neyman, и E. Pearson. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, (1933)